High-durability concrete response surface design method based on neural network

Abstract

The invention discloses a high-durability concrete response surface design method based on a neural network. According to the method, a high-durability concrete response surface prediction model based on a neural network is established based on environmental influence factors of a real marine service environment and composition characteristics of raw materials of building materials, prediction of key index parameters of durability of concrete is realized, iterative optimization is performed on the response surface model through an error function, and the prediction accuracy of the response surface model is improved. Influence factors of all input variables on concrete durability key index parameters are determined through sensitivity analysis, and optimization design of high-durability concrete in a real ocean service environment is guided.

Description

Technical Field

[0001] The invention belongs to the technical field of high-durability concrete design, and relates to a high-durability concrete response surface design method based on a neural network. Background Art

[0002] With the development of the marine economy, the construction of marine engineering projects such as ports and docks has put forward new requirements for the matching design of building materials and concrete structure performance. In the marine service environment, concrete structures will be affected by various environmental factors such as seawater erosion, salt spray, radiation, and wave erosion, and will face a very high risk of fatigue damage. Therefore, it is very important to carry out high-durability concrete optimization design based on the key factors affecting the service life of concrete to improve the service stability and service life of concrete in the marine environment.

[0003] The current design methods for high-durability concrete in marine service environments can guide the design and preparation of high-durability concrete to a certain extent, but there are still some shortcomings: on the one hand, the existing design methods for high-durability concrete mainly consider the influence of corrosive ions on the durability of concrete, and have not carried out design research on the multiple influencing factors of the service life of concrete in the actual service environment; on the other hand, traditional response surface design methods usually use methods such as Box-Behnken and quadratic regression design, which usually have low accuracy for complex nonlinear relationships and cannot achieve multi-objective precise output under multiple variables. Summary of the invention

[0004] The purpose of the present invention is to provide a high-durability concrete response surface design method based on a neural network, which realizes the high-durability optimization design and durability prediction of concrete on the basis of considering multiple environmental influencing factors of the real marine service environment and the characteristics of raw materials of building materials.

[0005] The technical solution for achieving the purpose of the present invention is as follows:

[0006] The neural network-based response surface design method for high-durability concrete includes the following steps:

[0007] S1. Determine the environmental factors in the real marine service environment;

[0008] S2. Determine the composition parameters of concrete raw materials;

[0009] S3. Select the evaluation index of concrete durability under the real marine service environment;

[0010] S4. Use the response surface experimental design method to establish a concrete durability experiment in a real marine service environment, and obtain the concrete durability evaluation index under different environmental factors and concrete raw material composition parameters in a real marine service environment;

[0011] S5. Establishing a response surface prediction model between the concrete durability evaluation index and the environmental factors and raw material composition parameters in the actual service environment based on a feedforward neural network; the feedforward neural network comprises an input layer, a hidden layer and an output layer; the environmental factors and the concrete raw material composition parameters in the actual marine service environment are input variables, and the concrete durability evaluation index is an output variable;

[0012] S6. Divide the response surface experimental data into a test set and a validation set, use the mean square error (MSE) to evaluate the prediction results of the response surface prediction model, and iteratively optimize the prediction model;

[0013] S7. Calculate the influencing factors of each input variable in the response surface prediction model through sensitivity analysis and determine the key influencing factors of concrete durability.

[0014] Furthermore, in S1, the environmental factors in the actual marine service environment include but are not limited to the concrete exposure time t (years) in the actual marine service environment, the annual average temperature T (°C), the chloride ion concentration in seawater (g / L), etc.

[0015] Furthermore, in S2, the concrete raw material composition parameters include but are not limited to ordinary Portland cement, water, different types of mineral admixtures (such as fly ash, mineral powder, silica fume, etc.), admixtures (such as water reducers), aggregate content and concrete water-cement ratio, etc.

[0016] Furthermore, in S3, the concrete durability evaluation index under the real marine service environment includes but is not limited to the chloride ion concentration on the concrete surface (%), the average chloride ion concentration on the concrete protective layer (%) and the chloride ion concentration on the steel bar surface (%), etc.

[0017] Furthermore, in S5, the number of hidden layers is usually 1 to 3, which is determined based on the number of input variables and the complexity of the model; the hidden layer includes h neurons, which are used to extract the features of the input data; for each neuron j in the hidden layer, the weighted sum is calculated by formula (1):

[0018]

[0019] Among them, x i is the input variable, w ij x i The input variable x i to the weight of hidden neuron j, b j is the bias of the neuron, Z j is the weighted sum of the jth neuron;

[0020] The Sigmoid activation function is used in the hidden layer for nonlinear transformation, and the activation value a of the neuron is calculated by formula (2): j :

[0021]

[0022] Furthermore, in S5, the weighted sum of the output is calculated by formula (3) and the activation function is applied to obtain the output variable y:

[0023]

[0024] Among them, w j is the weight of the output layer, and b is the bias of the output layer.

[0025] Furthermore, in S6, the number of iterations is between 100 and 1000.

[0026] Further, in S6, the mean square error L is calculated by formula (4):

[0027]

[0028] Among them, m is the number of samples, y k The actual values ​​of the key indicators of concrete durability in the real marine service environment. is the predicted value of the response surface prediction model based on feedforward neural network.

[0029] Furthermore, in S6, the weights and biases are updated through the back-propagation algorithm to minimize the loss function:

[0030]

[0031] Among them, σ is the learning efficiency, which is usually set between 0.001 and 0.1.

[0032] Furthermore, in S7, the influencing factors of each input variable in the response surface prediction model are calculated through sensitivity analysis to determine the key influencing factors of concrete durability, which are:

[0033] (1) Take the test set X test As a benchmark, the response surface prediction model of high-durability concrete based on feedforward neural network calculated the benchmark prediction value corresponding to the test set

[0034] (2) For each input variable X i Create data copy X temp And add a perturbation δ to the variable to perturb the input variable:

[0035] X temp (:,i)=X temp (:,i)+δ (6)

[0036] (3) The predicted value after disturbance is calculated based on the input variable after disturbance using the high durability concrete response surface model based on feedforward neural network.

[0037] (4) By calculating the baseline forecast value and the predicted value after disturbance The difference between the input variables is used to obtain the impact factor of each input variable (X i ):

[0038]

[0039] Compared with the prior art, the present invention has the following advantages:

[0040] Based on the environmental influencing factors of the real marine service environment and the composition characteristics of the raw materials of building materials, the present invention establishes a high-durability concrete response surface prediction model based on a neural network, realizes the prediction of key indicator parameters of concrete durability, iteratively optimizes the response surface model through an error function, and determines the influence factors of each input variable on the key indicator parameters of concrete durability through sensitivity analysis, so as to guide the optimal design of high-durability concrete under the real marine service environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 Visualize results for response surface models of concrete structure durability;

[0042] Figure 2 This is the distribution diagram of predicted values ​​and true values ​​of key indicators of concrete durability. DETAILED DESCRIPTION

[0043] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0044] Example 1

[0045] The neural network-based response surface design method for high-durability concrete includes the following steps:

[0046] S1. Determine the environmental factors under the actual marine service environment, including: concrete exposure time t (years), annual average temperature T (℃) and chloride ion concentration in seawater (g / L) under the actual marine service environment.

[0047] S2. Determine the raw material composition parameters of concrete, including: the amount of ordinary Portland cement (kg / m 3 ) Fly ash dosage (kg / m 3 ), Mineral powder dosage (kg / m 3 ), silica fume dosage (kg / m 3 ), water reducing agent dosage (kg / m 3 ), water consumption (kg / m3 ), fine aggregate dosage (kg / m 3 ), coarse aggregate dosage (kg / m 3 ), water-cement ratio.

[0048] S3. Select the chloride ion concentration (%) on the concrete surface under the real marine environment as the evaluation index of concrete durability under the real marine service environment.

[0049] S4. The response surface experimental design method is used to establish a concrete durability experiment in a real marine service environment, and to obtain concrete durability evaluation indicators under different environmental factors and concrete raw material composition parameters in a real marine service environment.

[0050] S5. A response surface prediction model between the concrete durability evaluation index and the environmental factors and raw material composition parameters under the actual service environment is established based on a feedforward neural network; the feedforward neural network includes an input layer, a hidden layer and an output layer; the environmental factors and concrete raw material composition parameters under the actual marine service environment are input variables, and the concrete durability evaluation index is an output variable.

[0051] There is one hidden layer, which includes 10 neurons, used to extract the features of input data. For each neuron j in the hidden layer, the weighted sum is calculated by formula (1):

[0052]

[0053] Among them, x i is the input variable, w ij x i The input variable x i to the weight of hidden neuron j, b j is the bias of the neuron, Z j is the weighted sum of the jth neuron;

[0054] The Sigmoid activation function is used in the hidden layer for nonlinear transformation, and the activation value a of the neuron is calculated by formula (2): j :

[0055]

[0056] The weighted sum of the output is calculated by formula (3) and the activation function is applied to obtain the output variable y:

[0057]

[0058] Among them, w j is the weight of the output layer, and b is the bias of the output layer.

[0059] S6. The response surface experimental data were divided into a test set and a validation set. The mean square error (MSE) was used to evaluate the prediction results of the response surface prediction model. The prediction model was iteratively optimized with 1000 iterations.

[0060] The mean square error L is calculated by formula (4):

[0061]

[0062] Among them, m is the number of samples, y k The actual values ​​of the key indicators of concrete durability in the real marine service environment. is the predicted value of the response surface prediction model based on feedforward neural network.

[0063] The weights and biases are updated through the back-propagation algorithm to minimize the loss function:

[0064]

[0065] Among them, σ is the learning efficiency, which is 0.01.

[0066] S7. The influencing factors of each input variable in the response surface prediction model were calculated through sensitivity analysis to determine the key influencing factors of concrete durability, specifically:

[0067] (1) Take the test set X test As a benchmark, the response surface prediction model of high-durability concrete based on feedforward neural network calculated the benchmark prediction value corresponding to the test set

[0068] (2) For each input variable X i Create data copy X temp And add a disturbance δ to the variable to perturb the input variable, setting δ to 10% standard deviation:

[0069] X temp (:,i)=X temp (:,i)+10%×std(X temp (:,i)) (6)

[0070] (3) The predicted value after disturbance is calculated based on the input variable after disturbance using the high durability concrete response surface model based on feedforward neural network.

[0071] (4) By calculating the baseline forecast value and the predicted value after disturbance The difference between the input variables is used to obtain the impact factor of each input variable (X i ):

[0072]

[0073] Specifically, in this embodiment, the response surface experimental design method is used to establish the durability experiment of concrete in a real marine service environment, and the durability evaluation index of concrete composed of different environmental factors and different raw materials is tested. There are 12 input variables, including: the amount of ordinary Portland cement (kg / m 3 ) Fly ash dosage (kg / m 3 ), Mineral powder dosage (kg / m 3 ), silica fume dosage (kg / m 3 ), water reducing agent dosage (kg / m 3 ), water consumption (kg / m 3 ), fine aggregate dosage (kg / m 3 ), coarse aggregate dosage (kg / m 3 ), water-cement ratio, exposure time (a), annual average temperature (℃), chloride ion concentration in seawater (g / L), and one output variable, which is the chloride ion concentration on the concrete surface (%);

[0074] Based on the feedforward neural network, a concrete durability prediction model under real marine service environment is constructed, and the corresponding relationship between multiple input factors and output factors is established;

[0075] Based on the concrete durability response surface prediction model in real marine service environment, 75% of the data in the response surface experiment were extracted as the training set, and 25% of the data were extracted as the validation set. The mean square error function was used to evaluate the model prediction results, and the concrete durability response surface prediction model was iteratively optimized.

[0076] Based on sensitivity analysis, the influence of each input variable on the model output is calculated to determine the influence of each input variable on the durability of concrete under real marine service environment, thus guiding the multi-objective optimization design of high-durability concrete under real marine service environment.

[0077] In this embodiment, Matlab software is used to construct a high-durability concrete response surface model based on a feedforward neural network, iteratively optimize the durability key indicator prediction model, and calculate the influencing factors of input variables, so as to obtain the key influencing factors affecting the key indicator parameters of concrete durability under the real marine service environment, thereby guiding the multi-objective optimization design of high-durability concrete.

[0078] Taking the response surface experimental design ratio and the real environmental factors of a certain area of ​​the ocean as an example, the dosage of ordinary Portland cement

[0079] (kg / m 3 ) Fly ash dosage (kg / m 3 ), Mineral powder dosage (kg / m 3 ), silica fume dosage (kg / m3 ), water reducing agent dosage (kg / m 3 ), water consumption (kg / m 3 ), fine aggregate dosage (kg / m 3 ), coarse aggregate dosage (kg / m 3 ), water-binder ratio, exposure time (a), annual average temperature (℃), and chloride ion concentration in seawater (g / L) are used as input variables, and chloride ion concentration on the concrete surface (%) is used as an output variable. Some response surface experimental data are shown in Table 1.

[0080] Table 1

[0081]

[0082] Matlab software was used to construct a high-durability concrete response surface model based on a feedforward neural network, iterative optimization of the prediction model for key indicators of concrete durability, and sensitivity analysis of input variable influencing factors. Matlab software is a scientific computing and numerical analysis software that provides an integrated development environment, including numerical calculation, data visualization, programming, and algorithm development functions. It is widely used in engineering design, numerical simulation and other fields, and will not be described in detail here.

[0083] Table 2

[0084]

[0085]

[0086] The high-durability concrete response surface model based on feedforward neural network uses mean square error (MSE) as the error function for iterative optimization, and uses sensitivity analysis to calculate the influencing factors of each input variable. The number of hidden layers is set to 1, the number of neurons is 10, the maximum number of iterations is 1000, and the learning rate is 0.01. For the 75% training set and the 25% validation set, the root mean square error is calculated by the mean square error function to be 0.17869. The distribution of the predicted value and the true value is shown in Figure 2As shown in Table 2, the influencing factors of each input variable are obtained. As can be seen from Table 2, on the one hand, there are positive and negative differences in the influencing factors of different input variables, indicating that there is a positive or negative correlation between different variables and the output variable. Taking the amount of ordinary Portland cement and exposure time as an example, the influencing factor of ordinary Portland cement is negative, indicating that increasing the amount of ordinary Portland cement is conducive to reducing the chloride ion concentration on the surface of concrete, that is, promoting the durability of concrete structures. On the contrary, the positive correlation between exposure time and surface chloride ion concentration indicates that extending the exposure time will have an adverse effect on the durability of concrete structures; on the other hand, there are differences in the absolute values ​​of the influencing factors of different input variables, indicating that different input variables have different degrees of influence on the durability of concrete structures in real marine service environments. Taking the amount of water reducer and the average annual temperature as an example, the absolute value of the influencing factor of the water reducer is 0.0022229, which is less than the absolute value of the shadow of the average annual temperature, 0.011104, indicating that compared with the amount of water reducer, the average annual temperature in the service environment of concrete structures has a more significant effect on the durability of concrete structures.

Claims

1. A neural network-based high-durability concrete response surface design method, characterized in that: The following steps are involved: S1. Determine the environmental factors in the real marine service environment; S2. Determine the composition parameters of concrete raw materials; S3. Select the evaluation index of concrete durability under the real marine service environment; S4. Use the response surface experimental design method to establish a concrete durability experiment in a real marine service environment, and obtain the concrete durability evaluation index under different environmental factors and concrete raw material composition parameters in a real marine service environment; S5. Establishing a response surface prediction model between the concrete durability evaluation index and the environmental factors and raw material composition parameters in the actual service environment based on a feedforward neural network; the feedforward neural network comprises an input layer, a hidden layer and an output layer; the environmental factors and the concrete raw material composition parameters in the actual marine service environment are input variables, and the concrete durability evaluation index is an output variable; S6. Divide the response surface experimental data into a test set and a validation set, use the mean square error to evaluate the prediction results of the response surface prediction model, and iteratively optimize the prediction model; S7. Calculate the influencing factors of each input variable in the response surface prediction model through sensitivity analysis and determine the key influencing factors of concrete durability.

2. The high durability concrete response surface design method according to claim 1, characterized in that: In S1, the environmental factors under the actual marine service environment are selected from at least one of the concrete exposure time, the annual average temperature and the chloride ion concentration in the seawater under the actual marine service environment.

3. The high durability concrete response surface design method according to claim 1, characterized in that: In S2, the concrete raw material composition parameters are selected from one or more of ordinary Portland cement, water, fly ash, mineral powder, silica fume, water reducing agent, aggregate content and concrete water-cement ratio in concrete.

4. The high durability concrete response surface design method according to claim 1, characterized in that: In S3, the concrete durability evaluation index under the real marine service environment is selected from one of the chloride ion concentration on the concrete surface, the average chloride ion concentration on the concrete protective layer and the chloride ion concentration on the steel bar surface.

5. The high durability concrete response surface design method according to claim 1, characterized in that: In S5, the number of hidden layers is 1 to 3; the hidden layer includes h neurons; for each neuron j in the hidden layer, the weighted sum is calculated by formula (1): Among them, x i is the input variable, w ij x i The input variable x i to the weight of hidden neuron j, b j is the bias of the neuron, Z j is the weighted sum of the jth neuron; The Sigmoid activation function is used in the hidden layer for nonlinear transformation, and the activation value a of the neuron is calculated by formula (2): j :

6. The high durability concrete response surface design method according to claim 1, characterized in that: In S5, the weighted sum of the output is calculated by formula (3) and the activation function is applied to obtain the output variable y: Among them, w j is the weight of the output layer, and b is the bias of the output layer.

7. The high durability concrete response surface design method according to claim 1, characterized in that: In S6, the number of iterations is between 100 and 1000.

8. The high durability concrete response surface design method according to claim 1, characterized in that: In S6, the mean square error L is calculated by formula (4): Among them, m is the number of samples, y k The actual values ​​of the key indicators of concrete durability in the real marine service environment. is the predicted value of the response surface prediction model based on feedforward neural network.

9. The high durability concrete response surface design method according to claim 1, characterized in that: In S6, the weights and biases are updated through the back-propagation algorithm to minimize the loss function: Among them, σ is the learning efficiency, which is usually set between 0.001 and 0.

1.

10. The high durability concrete response surface design method according to claim 1, characterized in that: In S7, the influencing factors of each input variable in the response surface prediction model are calculated through sensitivity analysis to determine the key influencing factors of concrete durability, specifically: (1) Take the test set X test As a benchmark, the response surface prediction model of high-durability concrete based on feedforward neural network calculated the benchmark prediction value corresponding to the test set (2) For each input variable X i Create data copy X temp And add a perturbation δ to the variable to perturb the input variable: X temp (:,i)=X temp (:,i)+δ (6) (3) The predicted value after disturbance is calculated based on the input variable after disturbance using the high durability concrete response surface model based on feedforward neural network. (4) By calculating the baseline forecast value and the predicted value after disturbance The difference between the input variables is used to obtain the impact factor (X i ):

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